Preheat the oven to 375°F (190°C).
Heat a skillet over medium heat and melt the butter. Add the chopped onion, chopped bell pepper, and minced garlic and sauté 2–3 minutes until softened.
While the vegetables soften, cut the chicken breast into 3/4-inch chunks and slice the andouille sausage into 1/2-inch rounds.
In a 3-quart baking dish, combine the dried rice, sautéed vegetables, chicken chunks, sausage slices, canned fire-roasted tomatoes (with juices), Cajun seasoning, and 1 cup of the shredded cheddar. Stir to mix evenly.
Pour the 3 cups of chicken broth over the mixture, then gently shake or tap the dish so the rice is submerged and ingredients settle evenly.
Cover the dish tightly with aluminum foil and bake in the preheated oven for about 60 minutes, or until the rice is tender and liquid is absorbed.
Carefully remove the foil and fluff the rice with a fork. Sprinkle the remaining 1 cup of shredded cheddar and the chopped scallions over the top.
Return the dish uncovered to the oven and bake 3–5 minutes more, until the cheese is melted. Serve warm.